The terms ‘shoal’, ‘swarm’ and ‘school’ are very frequently used in research on collective behaviours in animals. Pitcher’s definitions are accepted as the authority in the field but are based on a conceptual criterion of sociability. Without call into question the basis of these definitions, they do not provide tools to determine these behaviours quantitatively. To compare studies between populations, species, taxa or different experimental treatments, and between different authors, quantitative references are necessary. Quantitative measurements of collective behaviours can also test and validate the predictive capacity of computer models by comparing real data from nature so that different models can be compared. The first part of this paper succinctly reviews the definitions and meanings of these behaviours, with particular attention paid to quantitative aspects. This review underlines a series of conceptual confusions concerning these behavioural terms observed in the scientific literature and oral scientific communications. The second part reviews the quantitative parameters developed by biologists studying collective fish behaviours, mainly fish shoals, and by theoretical biologists and physicists studying computer modelling of collective behaviours. The parameters reviewed herein make no attempt to explain the mechanisms and causes that create a shoal, a swarm or a school, but rather try to describe these collective behaviours, and to connect local and global properties with individual and collective behaviours. Recent development over the last decade in technology, data processing capacity, cameras, and video tracking tools have provided the opportunity to obtain quantitative measures of collective dynamic behaviours in animals both rapidly and precisely.